login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A166261 Numbers n with property that sum of 120 successive primes starting with n-th prime is a square. 6

%I

%S 10917,11527,50923,73894,111468,118436,128662,139123,195234,249281,

%T 332863,435489,438080,482557,538373,542299,650254,679958,722145,

%U 803501,810871,820409,962582,970711,1003544,1027732,1030010,1190134,1204929,1305603,1636065,1689410

%N Numbers n with property that sum of 120 successive primes starting with n-th prime is a square.

%C Corresponding values of s = sqrt(Sum(prime(k), k=n..n+119)): (3734, 3846, 8660, 10602, 13248, 13690, 14318, 14936, 17934, 20458,...) = A166262.

%e a(1) = 10917: Sum_{i=0..119} prime(10917+i) = 3734^2 = A166262(1)^2,

%e a(2) = 11527: Sum_{i=0..119} prime(11527+i) = 3846^2 = A166262(2)^2.

%t PrimePi/@Select[Partition[Prime[Range[169*10^4]],120,1],IntegerQ[ Sqrt[ Total[ #]]]&][[All,1]] (* _Harvey P. Dale_, Jan 22 2019 *)

%o (PARI) lista(nn) = {pr = primes(nn); for (i=1, nn-119, s = sum(k=i, i+119, pr[k]); if (issquare(s), print1(i, ", ")););} \\ _Michel Marcus_, Oct 15 2013

%o (PARI) S=vecsum(primes(119)); p=0; q=prime(120); for(n=1,oo, issquare(S+=q-p) && print1(n","); q=nextprime(q+1); p=nextprime(p+1))} \\ It is about 25% faster to avoid "nextprime(p)" at expense of keeping the last 120 primes used in a vector p, using {my(i=Mod(0,120)); ...p[lift(i)+1]... i++}. - _M. F. Hasler_, Jan 04 2020

%Y Cf. A166262.

%Y Cf. A064397 (2 primes), A076305 (3 primes), A072849 (4 primes), A166255 (70 primes).

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 10 2009

%E a(30)-a(32) from _Michel Marcus_, Oct 15 2013

%E Edited by _M. F. Hasler_, Jan 04 2020

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 1 02:43 EST 2021. Contains 341732 sequences. (Running on oeis4.)